What is the integral of (sin(ax)-e^{x/b}) ?

The integral of (sin(ax)-e^{x/b}) is -1/a cos(ax)-be^{x/b}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (sin(ax)-e^{x/b})

\int (sin (a x) - e^{\frac{x}{b}}) d x

- \frac{1}{a} cos (a x) - b e^{\frac{x}{b}} + C

Solution steps

\int sin (a x) - e^{\frac{x}{b}} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int sin (a x) d x - \int e^{\frac{x}{b}} d x

\int sin (a x) d x = - \frac{1}{a} cos (a x)

\int e^{\frac{x}{b}} d x = b e^{\frac{x}{b}}

= - \frac{1}{a} cos (a x) - b e^{\frac{x}{b}}

Add a constant to the solution

= - \frac{1}{a} cos (a x) - b e^{\frac{x}{b}} + C

\int 5 x sec^{2} (3 x) d x

\int 8 - 2 x - x^{2} d x

\int \frac{2 + 8 x}{7 + 2 x + 4 x ^{2}} d x

\int \frac{4 x + 3}{4 x ^{3} + 8 x ^{2} + 3 x} d x

\int cos (π y) d y

What is the integral of (sin(ax)-e^{x/b}) ?
The integral of (sin(ax)-e^{x/b}) is -1/a cos(ax)-be^{x/b}+C